atof error

http://www.codeguru.com/forum/showthread.php?t=323835

Regards,

Paul McKenzie

Quote:

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Originally Posted by sandodo

Thanks! I searched, but didnot find the answer. Maybe not searching enough. :blush:

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1/3 cannot be represented by a decimal number, because 3 is not a divisor of 10.
Similarly, 1/5 cannot be represented by a binary float, because 5 is not a divisor of 2.

Numbers that can be represented by binary floats are sums of powers of two.
It's easy to see that these numbers can be expressed with this form:

integer*2**i where i is a negative or positive integer.

Thanks Paul McKenzie for the helpful link. :wave:

Quote:

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Originally Posted by SuperKoko

1/3 cannot be represented by a decimal number, because 3 is not a divisor of 10.
Similarly, 1/5 cannot be represented by a binary float, because 5 is not a divisor of 2.

Numbers that can be represented by binary floats are sums of powers of two.
It's easy to see that these numbers can be expressed with this form:

integer*2**i where i is a negative or positive integer.

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Thanks. the example of 1/3 cannot be represent by decimal number is very good.

However for

Code:

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integer*2**i

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, cannot understand...... :confused:

Quote:

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Originally Posted by sandodo

However for

Code:

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integer*2**i

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, cannot understand...... :confused:

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Basically, this means that the only decimal fractions that can be represented exactly in binary are sums of powers (negative or positive) of 2.

For example:

0.5 can be represented exactly in binary, since:

0.5 = 1/2 = 1 * 2^(-1) (where "^" means "to the power of"). The "**" that Superkoko mentioned is the same as "to the power or".

Similarly, 3/16 can be represented in binary exactly since:

3/16 = 3/(2*8) = 3/(2^(-3)).

So basically if the denominator is 1, 2, 4, 8, 16, 32, 64, etc. the number can be represented in binary exactly.

Regards,

Paul McKenzie

The ** is for "to-the-power". +ve as well as -ve.

Quote:

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Originally Posted by exterminator

The ** is for "to-the-power". +ve as well as -ve.

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Right.
Good thing that you mention it, since it wasn't obvious.

I used the ** operator, in order to avoid confusion with the C xor operator ^.
But, I probably caused confusion with this least used convention.

Thanks a lot to all of you. You guys are great.

All my best!